The content provides a comprehensive overview of the stability analysis and stabilization of linear systems with distributed delays (DDs). It begins by introducing the general framework of coupled differential-functional equations (CDFEs) to model systems with delays, and presents the Lyapunov-Krasovski˘ı stability criterion for CDFEs.
The main focus is on reviewing existing frequency-domain and time-domain approaches for the stability analysis of linear time-delay systems (LTDSs), with a particular emphasis on linear systems with DDs. Frequency-domain methods involve computing the spectral abscissa by finding the zeros of the characteristic equation, while time-domain approaches rely on constructing Lyapunov-Krasovski˘ı functionals (LKFs).
The content then outlines the research motivations and provides an overview of the subsequent chapters, which cover:
The proposed methods utilize the LKF approach and novel integral inequalities to address the stability and stabilization of linear systems with nontrivial distributed delays, considering dissipativity constraints.
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arxiv.org
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